The current invention relates to methods and apparatus for analyzing nonlinear data and particularly time-series nonlinear data derived from any of a variety of nonlinear processes or processes having a nonlinear component, and more particularly relates to methods and apparatus for detecting and measuring changes in states of nonlinear systems, conditions of nonlinear processes, and structure of nonlinear data.
Nonlinear processes, from which nonlinear data can be derived, are ubiquitous. The number and kind of such processes cannot be fully listed, but examples include: brain waves; heart waves;
electrical transients in power systems; fluid (air or water) flow over surfaces such as those of automobiles, airplanes, or submarines; weather and climate dynamics; machine tool-part interaction (e.g., tool chatter); nuclear reactor instabilities; fusion plasma instabilities; earthquakes; turbulent flow in conduits; fatigue and stress crack growth; and planetary or satellite motion. Applications in such fields as engineering, medicine, and research frequently require the ability to distinguish and/or quantify differences between apparently similar, but actually different, states in a nonlinear system. Inherent nonlinearity and high levels of noise in systems such as those described by example above make condition or state comparisons extremely difficult or even impossible through the use of linear or traditional nonlinear analyses. For example, conventional methods cannot detect differences in brain wave activity between baseline, pre-seizure, seizure, or postseizure states. Timely monitoring and detection of changes in the state of a nonlinear system can be used to provide adequate metrics for the basic purpose of better understanding the process. From a practical standpoint, detecting and measuring condition changes can be used predictively, for example, to detect the imminent onset of a seizure or an imminent failure of the system or a part thereof. The process may need to be monitored in real-time or near real-time for the monitoring to be of use. Conventional methods, in those instances where they can be of use, however, require a relatively large amount of data and a relatively large amount of computing power. This makes real-time monitoring difficult or impossible simply because of the cost or availability of the data acquisition, storage, and manipulation means.
Even existing nonlinear methods of monitoring process data cannot always detect differences on the scale required for a given process. In some cases, this is simply because the method is insufficiently sensitive, or the measurements of the changes in state or condition are not robust enough to be reliable. In other cases, the methods require large amounts of storage and computing capability that are not available as a practical matter, or at all.
It is an object of the current invention to overcome the above-mentioned problems by providing a method and apparatus for detecting, measuring, and monitoring condition changes in nonlinear processes and systems.
It is also an object of the current invention to provide a method and apparatus capable of providing an indication of a difference between two similar but different states in nonlinear processes and systems.
It is a further object of the current invention to provide a means of monitoring and comparing nonlinear data from a process or system to provide an indication of a change in state or condition of the process or system.
It is moreover an object of the current invention to provide a method and apparatus of measuring and detecting trends in the condition or state of a nonlinear process or system.
In accordance with the foregoing objectives, it is also a particular object of this invention to provide a method and apparatus for filtering, monitoring, and comparing nonlinear data from a process or system to provide an indication of a change in state or condition of the process or system, wherein said filtering, monitoring, comparing, and detecting are based solely on the data derived from the process or system in the absence of any assumptions about or models for the underlying process or system dynamics.
In a specific aspect of the invention, it is an object thereof to provide a method and apparatus for filtering, monitoring, and comparing nonlinear data from EEG sensors, and particularly from a single channel of scalp EEG, to detect and monitor nonseizure, pre-seizure, and seizure epileptic states such that a forewarning of a seizure may be provided.
The invention accomplishes the foregoing and other objects by providing a method in which nonlinear data from a process or system is acquired, monitored, and filtered. The filtered data are then used to represent the system dynamics as connected phase-space points, in turn represented by 2n-dimensional vectors within a windowed data set. A distribution function is calculated for each windowed data set to capture the occurrence frequency in the discretized (connected) phase-space. Condition change is detected, monitored, and measured by comparing the distribution functions via dissimilarity metrics, specifically using "khgr"2 statistics and L1 distance. The dissimilarity measures are renormalized to provide a consistent comparator for robust and reliable detection of changes or trends. The method can be incorporated into apparatus including a data collector, a processor, and an output device enabling real-time and near real-time assessment of data. The apparatus can be made automatic, that is, made to provide an output only when a change or given magnitude of change is detected.
The method provides a new, timely, accurate, and robust means for measuring condition change in nonlinear data. It is model-independent and, by appropriate selection of comparison criteria, can be used to detect or measure any selected amount or degree of change in a system.
In accordance with one aspect of the invention, the foregoing and other objects are achieved by a method for detecting or measuring condition or state changes in a nonlinear process or system, or monitoring the condition or state of a nonlinear process or system. The method comprises the following steps. A channel of nonlinear data from the process or system is provided. The data, referred to herein as e-data, may be provided in real-time or near real-time or may be from a means for data storage. While the e-data is typically a time serial sequence of nonlinear measures, the method is not limited to the use of time serial sequence measures, but may be used with data sequenced by a means other than time. The e-data is then filtered by means of a zero-phase quadratic filter that removes artifacts (f-data) from the data without distorting the phase or amplitude of the e-data. The resulting artifact-filtered data is referred to as g-data. The g-data is serially discretized into windowed cutsets. For time serial data, the cutsets are time-windowed cutsets. Within each cutset, the g-data are processed to create an n-dimensional phase-space representation of the data, described as a discrete n-dimensional vector. The method connects the flow of each phase-space point into the subsequent phase-space point, as a single connected-phase-space point, which is represented by a discrete 2n-dimensional vector. A distribution function tabulates the occurrence frequency of each discrete (connected) phase space vector for each cutset. The distribution function for a first selected cutset is compared with the distribution function for a second selected cutset whereby the differences between the dynamics for each compared cutset can be detected and measured. An output is then provided indicative of the dissimilarity.
In another aspect of the invention, one or more of the cutsets mentioned above can be used to define a basecase for the process. Using the foregoing method, the basecase cutset(s) can be used to generate a series of representative distribution functions against which all other (testcase) cutsets are compared, thus enabling an output indicative of a relative change in state or condition. The distribution function of the j-th testcase cutset can then be compared to the distribution function of each basecase cutset. The resulting measures of dissimilarity may be averaged over the basecase cutsets. When the comparison between the distribution functions of the unknown and basecase cutsets shows a significant difference, an output signal can be generated indicative of the difference or indicative of the fact of a difference. Alternatively, the base case cutset(s) can be used to establish a trend, the comparison thereafter enabling detection and/or measurement of a deviation in trend.
In another aspect of the invention there is provided apparatus comprising processing means capable of performing the method steps set forth above. The apparatus can also comprise the data sensing means or a means for receiving at least one channel of data. The apparatus also comprises an output means for providing an indication of the detection, measurement, or monitoring of the changes in condition of the process or system.
The method and apparatus according to the current invention enable a large reduction in the amount of data storage and data processing required because the distribution functions derived, and the comparison of the distribution functions, utilize only the populated states within each cutset. This improvement alone enables at least a many hundred-fold decrease in the amount of computing power required. This reduction in turn means that the method may be performed on a programmable general purpose personal computer. Alternatively, the method and apparatus may utilize a relative small amount of dedicated circuitry. Because such computers are widely available and relatively inexpensive, monitoring and analyses of data can be performed on-site and in real time.